Excerpt from On the Partial Difference Equations, of Mathematical Physics Nyo-7689 of arbitrarily high order tends to the corresponding deriva tive. Nowhere do we assume the existence of the solution to the differential equation problem on the contrary, we obtain a simple existence proof by using the limiting processi. For the case of elliptic equations convergence is obtained independently of the choice of mesh, but we will find that for the case of the initial value problem for hyperbolic equations, convergence is obtained only if the ratio of the mesh widths in different directions satis fies certain inequalities which ih turn depend on the position of the characteristics relative to the mesh. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.